A sample of 76 items manufactured by a machine contains 13 defective items and the rest are non-defective. If 15 items are selected at random, what is the probability that fewer than 2 of these are defective?

A sample of 76 items manufactured by a machine contains 13 defective items and the rest are non-defective. If 15 items are selected at random, what is the probability that fewer than 2 of these are defective?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Expert Solution

Step 1

Total number of items, N = 76 items

Total number of defectives , K = 13 defective items

Sample Size selected , n = 15 items

Here, Hypergeometric distribution will be used to calculate the probability

The formula for Hypergeometric probability is :

$\Pr(X = k) = \frac{\left( \begin{matrix} K \\ k \end{matrix}\right) \times \left( \begin{matrix} N-K \\ n-k \end{matrix}\right)}{\left( \begin{matrix} N \\ n \end{matrix}\right)}$

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